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Help on 3-D Geometry problems

by crackgmat007 » Wed Apr 29, 2009 4:07 pm
Pls help me solve the below 3-D geometry problems...thanks

1) What is the volume of a certain cube?
1. The sum of the areas of the faces of the cube is 54.
2. The greatest possible distance between two points on the cube is 3*sqrt of 3

OA - D

2) A ball with a diameter of 10 cm is inscribed inside a rectangular box so that it touches all internal faces of the box. What is the volume trapped between the box and the ball?
1. The box is a cube
2. The surface are of the box is 600 cm^2

OA-D

3) A rectangular box is inside a cylinder. Both the width and length of the box is 2 cm. What is the volume of the cylinder?
1. The volume of the box is 20 cm^3
2. The radius of the cylinder is sqrt of 2

OA - A
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by gauravgundal » Thu Apr 30, 2009 2:19 am
1) What is the volume of a certain cube?
1. The sum of the areas of the faces of the cube is 54.
2. The greatest possible distance between two points on the cube is 3*sqrt of 3

OA - D

Yes I think Answer is D

Statement 1: The sum of the areas of the faces of the cube = 6L^2
L -Length of the side of cube
Vol = L^3

Statement 2 :
The Greatest Possible distance=
L^2 + L ^2 + L^2 =(3sqrtof3)^2
L=3
Vol=L^3
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by gauravgundal » Thu Apr 30, 2009 2:33 am
2) A ball with a diameter of 10 cm is inscribed inside a rectangular box so that it touches all internal faces of the box. What is the volume trapped between the box and the ball?
1. The box is a cube
2. The surface are of the box is 600 cm^2

OA-D

Yes D is correct

Statement 1: As the ball touches all int. faces of the box The Dia. of ball is equ to side of the cube .
Vol Trapped = Vol of Box[10^3] - Vol of Ball [(4/3)*pie*5^3]

Statement 2: As ball touches all the internal faces of the box .The box should be a cube.
Surface area of cube = 6*L^2=600
: L = 10

Vol Trapped = Vol Trapped = Vol of Box[10^3] - Vol of Ball [(4/3)*pie*5^3]
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by mike22629 » Thu Apr 30, 2009 10:02 am
Important equation to know for GMAT and it pertains to question 1.

First of all, the longest distance in a cube is the diagonal from the top to the bottom.

The equation for diagonal = s*(sq root of 3)

Since the question tells you that the longest point is 3 * sqrt of 3

Set them equal

s*(sqrt of 3) = 3*(sqrt of 3)

s = 3
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by harrycool » Sat Apr 17, 2010 6:19 pm
Can anyone help me with Q.3

the box is inside the cylinder . there is no clue where the box touches the cylinder . So i feel the answer should be E not A
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by student22 » Sat Apr 17, 2010 6:28 pm
You're right for question 3. Nowhere does it mention that the box touches the cylinder.

Also, a more important point, the question doesn't mention that height of the cylinder. So, even if the box fits snuggly within the cylinder, the cylinder could be very tall.

Imagine, putting a box inside of a Pringles can, to see what I mean.

E. Not sufficient.
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Square peg in a round hole

by kstv » Sat Apr 17, 2010 9:12 pm
gauravgundal wrote:2) A ball with a diameter of 10 cm is inscribed inside a rectangular box so that it touches all internal faces of the box. What is the volume trapped between the box and the ball?
1. The box is a cube
2. The surface are of the box is 600 cm^2
OA-D
Yes D is correct
Statement 1: As the ball touches all int. faces of the box The Dia. of ball is equ to side of the cube .
Vol Trapped = Vol of Box[10^3] - Vol of Ball [(4/3)*pie*5^3]
Statement 2: As ball touches all the internal faces of the box .The box should be a cube.
Surface area of cube = 6*L^2=600
: L = 10
Vol Trapped = Vol Trapped = Vol of Box[10^3] - Vol of Ball [(4/3)*pie*5^3]
See the bold part , then 1. The box is a cube is not necessary. Why not option B.
Infact do u need 1. and 2. to find the volume ?
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by eaakbari » Sat Apr 17, 2010 11:32 pm
(1) - D, As gaurav explained

(2) - A, In the second statement we do not know its a cube,so 2(lh +2lb +bh) = 600 which does not help us find the volume.

(3) - E, we do not know whether box is touching cylinders edge or whether its inscribed, etc. So either question has something missing or ANSWER E
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by iamtensai » Mon Apr 19, 2010 3:32 pm
Agreed:
Q1: D
Q3: E (but if we are given the fact that the cylinder and the box have the same height, the answer would be A)

My take for Q2: D

For question 2, I believe there is a little trick.
Since the question stated that the ball "touches all internal faces of the box", then it is implied that the box is a cube. With just the information in the question (i.e. diameter of 10 cm), we can solve for the problem.

Thus, regardless what's in (1) and (2), the data is sufficient. (although both statements provide redundant information)
Logically, we should pick answer D since in either situation, we are sufficient.
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by eaakbari » Mon Apr 19, 2010 9:17 pm
iamtensai wrote:Agreed:
Q1: D
Q3: E (but if we are given the fact that the cylinder and the box have the same height, the answer would be A)

My take for Q2: D

For question 2, I believe there is a little trick.
Since the question stated that the ball "touches all internal faces of the box", then it is implied that the box is a cube. With just the information in the question (i.e. diameter of 10 cm), we can solve for the problem.

Thus, regardless what's in (1) and (2), the data is sufficient. (although both statements provide redundant information)
Logically, we should pick answer D since in either situation, we are sufficient.
Hmm, Maybe you are right, but two redundant statements on the GMAT, thats funny. Whats the source of the question
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by kstv » Wed Apr 21, 2010 2:18 am
iamtensai wrote:Agreed:
Q1: D
Q3: E (but if we are given the fact that the cylinder and the box have the same height, the answer would be A)
My take for Q2: D
For question 2, I believe there is a little trick.
Since the question stated that the ball "touches all internal faces of the box", then it is implied that the box is a cube. With just the information in the question (i.e. diameter of 10 cm), we can solve for the problem.
Thus, regardless what's in (1) and (2), the data is sufficient. (although both statements provide redundant information)
Logically, we should pick answer D since in either situation, we are sufficient.
Any corelation with ?
https://www.beatthegmat.com/round-hole-i ... 56306.html
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by eaakbari » Wed Apr 21, 2010 5:06 am
kstv wrote:
iamtensai wrote:Agreed:
Q1: D
Q3: E (but if we are given the fact that the cylinder and the box have the same height, the answer would be A)
My take for Q2: D
For question 2, I believe there is a little trick.
Since the question stated that the ball "touches all internal faces of the box", then it is implied that the box is a cube. With just the information in the question (i.e. diameter of 10 cm), we can solve for the problem.
Thus, regardless what's in (1) and (2), the data is sufficient. (although both statements provide redundant information)
Logically, we should pick answer D since in either situation, we are sufficient.
Any corelation with ?
https://www.beatthegmat.com/round-hole-i ... 56306.html
I did see the other post kstv, but IMO iamtensai is correct here because the question mentions rectangular box which would have to imply its a square. If it said quadrilateral, answer would have been different.
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by Stuart@KaplanGMAT » Wed Apr 21, 2010 9:58 am
crackgmat007 wrote: 1) What is the volume of a certain cube?
1. The sum of the areas of the faces of the cube is 54.
2. The greatest possible distance between two points on the cube is 3*sqrt of 3
Cubes, like spheres, are very simple shapes, since they involve only 1 dimension (the length of a side for a cube, the radius for sphere).

Here's the application of that concept to DS:

If you know 1 concrete piece of information about a cube or a sphere, you can answer any question about the shape.

Since each of (1) and (2) provides a concrete piece of information about the cube, each is sufficient alone.

Note that the same principle applies to squares and circles.
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by Stuart@KaplanGMAT » Wed Apr 21, 2010 10:06 am
crackgmat007 wrote: 2) A ball with a diameter of 10 cm is inscribed inside a rectangular box so that it touches all internal faces of the box. What is the volume trapped between the box and the ball?
1. The box is a cube
2. The surface are of the box is 600 cm^2
What's the source of this question? It would never appear as written on the actual GMAT.

As others have noted, the only way to satisfy the conditions in the question stem is for the box to be a cube. If we know that the box is a cube and we have the diameter of the ball, we can solve the question without recourse to the statements.

On the GMAT, the question is never answerable just from the question stem.
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